Zac Goldsmith is like Judi Dench. This similarity would never have occurred to me, but was pointed out by Tania Mathias, who last May achieved one of the most dramatic results of election night, turning Vince Cable out of Twickenham and converting his Lib Dem majority of 12,140 into a Conservative majority of 2,017.

Goldsmith, who captured the neighbouring constituency of Richmond Park from the Lib Dems in 2010, increased his own majority by an even larger amount, so it now stands at 23,015.

Mathias is in no doubt why this happened: “As soon as Zac meets people they’re on board. It’s like Judi Dench – good on film, breathtaking on stage.”

This was amazingly good advance billing for Goldsmith, and I wondered whether he would live up to it. Some Conservatives are worried that their London mayoral candidate is too laid back, too languid, too softly spoken and polite, too lacking in hunger and aggression to take on the Labour candidate, Sadiq Khan, whom the bookies and pollsters put ahead.

Iain Dale, in his latest ConHome column, went so far as to write of Goldsmith: “He looks as if he’d rather be anywhere else but doing what he’s doing…Cameron needs to give Zac a lesson on how to appear being ‘pumped up’.”

On a wet Saturday morning with a bitter wind blowing the rain in one’s face, not everyone would have wanted to be in Whitton High Street, a 1930s parade of shops one stop west of Twickenham on the railway. But Mathias, as the local MP, had turned out with at least two dozen Conservative activists, waiting for Goldsmith to arrive.

We took shelter in the local campaign headquarters, housed in Ultralux, a business selling windows. Mathias related in a steely tone how she vanquished Vince: “He was someone who’d been here for a very long time and didn’t realise his policies were no longer relevant. He was out of touch with people’s needs.”

Goldsmith arrived looking as if this was just where he wanted to be: he reminded me of a sportsman so caught up in the joys of the chase that he thinks nothing of its hardships.

In a short speech he thanked his followers for turning out on such a filthy day, and announced the latest news: “Sadiq Khan is on the run. He’s just pulled out of the Andrew Marr programme.”

Mathias made a clucking noise. Laughter. Goldsmith declared that Khan “is sick of having to defend the indefensible”, namely his promise to freeze transport fares for four years, which leaves a “£2 billion black hole” in Transport for London’s accounts, which Khan is unable to explain how he will fill.

“We are up against someone who is on the slide,” Goldsmith went on. “And we’ve won on Heathrow. Just for the record, we’ve won on Heathrow.”

“Better, not bigger,” Mathias interjected.

“As the Prime Minister said six years ago,” Goldsmith remarked in an ebullient tone. He has long been a prominent opponent of Heathrow expansion, and hopes this will demonstrate to voters that he does not bend to every passing breeze.

Khan was first in favour of expanding Heathrow, then turned against it.

We went out into the rain. Goldsmith explained as he strode along that “transport is a housing issue”, because only by improving transport links can one develop various areas where tens of thousands of houses need to be built.

At the first house in a road where the team were distributing leaflets, Goldsmith rang the bell, and as we waited, recalled with amusement the reaction he got from the very first householder he ever canvassed: “I’d rather eat my own shit than vote for a Tory.”

But the woman who answered the door was desperate to talk about parking. Her street has become a nightmare because commuters fill it with their cars before catching the train to central London. Goldsmith explained that if she gets 50 per cent of the residents to agree to a change in the parking rules, something can be done.

Later, over a cup of coffee, Goldsmith enlarged on his attack on Khan’s pledge to freeze fares: “He’s made a very stupid promise. Either he has no intention of delivering on it, or it would be catastrophic for London.”

Goldsmith believes voters will realise Khan’s promise “is just not credible”. He said that if Tessa Jowell had become the Labour candidate, things would have been different: “She’s a very decent person. I don’t think you could say it would be a catastrophe if Tessa Jowell was elected.”

But Khan flip-flops on everything: “On every issue of substance his position has changed for the sake of expediency.” The mansion tax, and Jeremy Corbyn, are recent conspicuous examples: both of these Khan favoured and then denounced.

In a piece about the Labour candidate for ConHome, I began: “Sadiq Khan is a more formidable politician than I realised before writing this profile. He possesses a remarkable ability to understand what an audience wants to hear, and an almost unbounded willingness to say it.”

Goldsmith intends to turn this willingness to say what people want to hear into Khan’s fatal weakness: a sure sign that he cannot be trusted.

But, I objected, some Londoners might like the idea of electing a Moslem mayor, as a demonstration of how tolerant the city is. This suggestion pained Goldsmith. He pointed out that no mayor can, as an individual, represent all Londoners, or even all members of a particular faith: “It is the job of the mayor to hold London together. Unlike Paris, we are on the whole a harmonious city.”

I was struck during this conversation by Goldsmith’s intense competitiveness. This quality is obscured from some observers by his good manners. The same mistake is often made about David Cameron. People do not realise how ambitious these Etonians are, and how determined to do whatever is needed to win.

Khan has a fight on his hands, for Goldsmith too is a more formidable politician than even some Conservatives have realised. Mathias is right that this quality comes across more strongly when one meets Goldsmith in the flesh, than when one sees him on television.

But there are 80 days still to go in this campaign, which is a long time for Khan to defend himself against the charge of untrustworthiness. It is possible that the Labour man will show, by the staunchness with which he rebuts criticism, that he is actually a dependable figure. But his record, in his constituency of Tooting as well as more widely, suggests that he tends to react badly to attempts to subject him to scrutiny.

Whitton is close to Goldsmith’s own constituency, so one would expect people there to be well-disposed towards him, and to see him as a winner. But a local Tory explained why he expects Goldsmith to beat Khan: “People in the suburbs are probably really quite frightened of a Khan mayoralty, what it will do to them personally, and whether if he were to put through his extraordinary policy of freezing fares, it would mean they had to pay higher taxes.”